
Proof of Prime number
Hello, could anyone give me some hints to do these following questions? Any help will be greatly appreciated, thanks (Wink)
a) Let a and n be integers greater than 1. Prove that $\displaystyle a^n 1$ is prime only if $\displaystyle a = 2$ and n is prime.
b) Show that $\displaystyle 2^n + 1$ is prime only if n is a power of 2.

a) $\displaystyle a^n1=(a1)\cdot{\left(1+a+...+a^{n1}\right)}$ so what happens if $\displaystyle a1>1$ ? (use this same identitychanging a to prove that n has to be prime)
b) note that $\displaystyle
a^{2k + 1} + 1 = \left( {a + 1} \right) \cdot \left( {1  a + a^2 \mp ... + a^{2k} } \right)
$ now suppose that $\displaystyle n$ has an odd divisor $\displaystyle d$ and write $\displaystyle
\left( {2^{\tfrac{n}
{d}} } \right)^d + 1 = 2^n + 1
$